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= Perception of Loudness and Envelopment in Concert Halls = Listening to music in a live setting at a concert hall can bring the listener to experience the music in a more interactive way than trying to recreate this setting at home using traditional loudspeakers. Specifically, when listening to symphonic music in a concert hall, the perception of the musical dynamics is directly coupled with the concert hall acoustics. This coupling has a direct impact on how a listener perceives the loudness and envelopment of the symphonies depending on where they are positioned in the concert hall. When listening to symphonic music in concert halls, the strongest factors affecting the perception of the sound is the source's loudness and width of envelopment. Given the aforementioned effects, additional research in the relationship between a listener’s perception of loudness, sound envelopment, and music dynamics in a given concert hall will provide insight on unknown effects that concert hall architecture has.

A recent study titled ‘Perception of loudness and envelopment for different orchestral dynamics’ set out to identify the perception of loudness and envelopment for different orchestral dynamics. This study was derived by previous studies regarding the loudness of concert halls. Specifically, the study titled ‘Perception of music dynamics in concert hall acoustics’ evaluated the perception of the loudness and width of envelopment when playing orchestral tunes at different dynamic levels with respect to the frequency spectrum. The new aforementioned study is seeking to replicate the previous experiment performed in 2016 by examining the level dependent loudness and envelopment differences by replicating the ordering of halls at different orchestral dynamics. Both studies used the same concert halls. This article will replicate the nomenclature of the halls: Berlin Konzerthaus (BK), Berlin Philharmonie (BP), Helsinki Musiikkitalo (HM), and Munich Herkulassaal (MH). A figure outlining the floor plans, seating arrangements and sections of all four concert halls can be seen in the appended document at the bottom of the article. This article will evaluate the previous empirical study finding the perceptual loudness and envelopment of these concert halls and compare them to a revised experiment that replicates the former experiment and builds on it by taking orchestral dynamics into account. This is an active area of study for acoustical and structural engineers that has been given much attention since the development of reverberation times within structures. Note that the 2016 study evaluated two additional concert halls - this article focuses on the four shared between the two.

Background
Concert hall acoustics are coupled with the viewers perception of the sound being presented. A sound source injects acoustic energy into a room and the room surfaces absorb the injected acoustic energy. Not all of this acoustical energy can be absorbed instantaneously, thus the room will reach a steady state. After the source is turned off, there is a time in which the acoustic energy will die out. This effect is used by structural engineers and acousticians to calculate the time in which the energy in the room will decrease by 60dB. This is known as the $$T_{60}$$ reverberation time. Before Sabine had developed room reverberation concepts, buildings were architecturally designed after functional designs previously. That is, acoustical properties of buildings were not taken into account until Sabine developed room reverberation $$T_{60}$$ reverb times.

Due to human hearing anatomy, we perceive certain frequency bands as quieter at certain dynamic levels than others. This is referred to as the A-weighting hearing curve. Kinsler defines the A-weight curve $$L_A$$ where each frequency is assigned a weight that is related to the sensitivity of the ear at that weight. Below is a table of typically encountered noises and their A-weight levels. A visualization of the A-weighted curve can be seen in the frequency response plot titled Human Hearing Filter Characteristics at the end of the article. The A-weighting image depicts the frequency response of the non-linear filters that are inherent with human hearing anatomy, and thus, affect the results of the acoustics hall experiments. Table 1 and Figure 2 are sourced from Fundamentals of Acoustics.

Survey of Perception Experiments Across Varying Concert Halls
Several studies have been performed in the past decade with an emphasis on the effects of perceived loudness and overall sense of envelopment while experiencing a musical performance in a concert hall. Concert hall acoustics are distinctly coupled with how a person experiences the music. Seating position, orchestral dynamic range, reflections and reverberations, and direction are just some of the key factors presented in the below studies that can affect the perception of a live performance.

Purpose
The author of this journal article iterates that the current research does not explore the effects of dynamic range thoroughly as an attributing factor to the perception of acoustic hall loudness. In previous studies, it was discovered that room acoustics are inseparably coupled with a listeners perception of loudness, timbre, and reverberation; where reverberation dictates the former two properties of music tonal perception. Pätynen also goes on to cite research stating that the high frequency overtones are overemphasized in concert hall acoustics.

Results and Discussion
As mentioned previously, the proposed factor in the perception of loudness was the music source width and the spaciousness of the acoustic hall. The results here found that was not the entire story - that is, the dynamic range of the source sound dominates the other loudness dependent factors for audio perception. Additionally, the perceived loudness was dominated at the front of the stage by direct sound and the lateral reflections did not have as much of an impact. Perceptual differences were accentuated as you were further away from the stage. Increased distance from the stage allowed for stronger lateral reverberation reflections.

Purpose
Lokki’s research presents an experiment that evaluates the perception of loudness and envelopment by auralizing musical passages in four separate orchestral dynamics, pianissimo, piano, forte, and fortissimo. The study here is focused on perceived loudness differences based on the varying orchestral dynamic ranges from the symphonic pieces.

Discussion
The results of the experiment of playing the pieces show that the small shoe-box shaped concert halls were much louder and enveloping than the vineyard style or raked style concert halls. However, unlike previous research, there were interesting dynamics that occurred between the separate halls that have not been documented in previous research. Lokki found that different orchestral dynamics pitted the concert halls differently than otherwise thought.

Loudness
The perception of loudness varies across concert halls due to their architectural acoustic qualities. Both Lokki and Pätynen state that shoebox concert halls rate much louder and more enveloping than raked style or vineyard style concert halls. However, Lokki has found in their 2020 study that there are differences in commonly accepted perceptions of loudness in varying concert halls then in previous studies. Specifically, the study done in 2020 by Lokki incorporated different orchestral dynamics (pianissimo, piano, forte, fortissimo) where the orchestral dynamics includes voice and instruments. Pätynen and Lokki have done previous experiments to the 2020 study, only the difference here is that the joint study in question done in 2016 focused on incorporating the frequency spectrum of the signal in tandem with the seating position. Pätynen and Lokki observed the perception of the test subjects in different seating positions and the relative loudness. Lokki’s study performed in 2020 found that orchestral dynamic ranges have a significant impact on the perceived loudness and overall envelopment. This was alluded to in the previous experiment where the musical piece presented in Pätynen’s study was a crescendo piece with orchestral dynamics rising from piano to forte fortissimo.

Envelopment
While the results outlined in the Loudness section become more concrete with Lokki’s study emphasizing orchestral dynamic range, the envelopment results mostly agreed with previous studies including Pätynen’s 2016 study on perceiving music in concert hall acoustics, but there were some differences. Lokki’s study found that the Berlin Konzerthaus concert hall had a significant improvement on the sense of envelopment that wasn’t as pronounced as in the 2016 study by Pätynen, but the results still come to the same conclusion. The 2020 study also found that the sense of envelopment in fortissimo was also greater in the Berlin Konzerthaus than in the Helsinki Musiikkitalo concert hall in spite of the fact that the perceived loudness of HM projected the opposite. The envelopment results for HM do agree with previous results done by Pätynen and Lokki in a 2015 study.

Summary
Researchers such as Tapio Lokki and Jukka Pätynen are forerunners in the ongoing investigation of how concert hall acoustics affect our human perception of loudness and envelopment. While there are many factors that have been documented and discovered empirically, there are many more to be found. This area of research covers both psychological and several engineering disciplines including structural, civil, and electrical engineering. Additional information can be found on the perceptual factors stemming from a study done in 1991 by John A. Sloboda. This study focuses on the emotional responses of music stimulation and how our bodies unconsciously react to different musical structures including shiver, goose pimples, or the feeling of a lump in the throat.

Conclusions
Listening tests were used to study the acoustics of concert halls and the perceived loudness and sense of envelopment using loudspeaker arrays to simulate a live orchestra playing. The study performed by Pätynen in 2016 emphasized the spectral content of the signal coupled with the acoustics of the concert halls dictated the perceived loudness and envelopment. Pätynen’s test included a crescendo that ranged dynamically from piano to forte fortissimo that ultimately factored into the final results. It wasn’t until Lokki’s study in 2020 that took a more focused approach on the orchestral dynamics effects on perceived loudness and sense of envelopment. The results of the 2020 study on perception agreed on an overarching scale the previous listening results in the 2015 and 2016 studies by Pätynen and Lokki, however the results in the 2020 study showed that the orchestral dynamics have more effect than was given credit to in the latter two studies.